Comparative Expressivity for Structured Argumentation Frameworks with Uncertain Rules and Premises
This work addresses a theoretical gap in argumentation research by comparing expressivity across models, but it is incremental as it builds on existing trends without broad practical impact.
The paper tackled the problem of modeling qualitative uncertainty in formal argumentation by grounding uncertainty in structured components like rules and premises, and introduced a notion of expressivity to compare abstract and structured models, presenting both negative and positive results that affect frameworks such as incomplete abstract argumentation and ASPIC+.
Modelling qualitative uncertainty in formal argumentation is essential both for practical applications and theoretical understanding. Yet, most of the existing works focus on \textit{abstract} models for arguing with uncertainty. Following a recent trend in the literature, we tackle the open question of studying plausible instantiations of these abstract models. To do so, we ground the uncertainty of arguments in their components, structured within rules and premises. Our main technical contributions are: i) the introduction of a notion of expressivity that can handle abstract and structured formalisms, and ii) the presentation of both negative and positive expressivity results, comparing the expressivity of abstract and structured models of argumentation with uncertainty. These results affect incomplete abstract argumentation frameworks, and their extension with dependencies, on the abstract side, and ASPIC+, on the structured side.